Observational Constraints on Direct Electron Heating in the Hot Accretion Flows in Sgr A* and M87

An important parameter in the theory of hot accretion flows around black holes is δ , which describes the fraction of “viscously” dissipated energy in the accretion flow that goes directly into heating electrons. For a given mass accretion rate, the radiative efficiency of a hot accretion flow is determined by δ . Unfortunately, the value of δ is hard to determine from first principles. The recent Event Horizon Telescope Collaboration (EHTC) results on M87* and Sgr A* provide us with a different way of constraining δ . By combining the mass accretion rates in M87* and Sgr A* estimated by the EHTC with the measured bolometric luminosities of the two sources, we derive good constraints on the radiative efficiencies of the respective accretion flows. In parallel, we use a theoretical model of hot magnetically arrested disks (MADs) to calculate the expected radiative efficiency as a function of δ (and accretion rate). By comparing the EHTC-derived radiative efficiencies with the theoretical results from MAD models, we find that Sgr A* requires δ ≳ 0.3. A similar comparison in the case of M87* gives inconclusive results as there is still a large uncertainty in the accretion rate in this source.